Identify the correct statement : - Vidyadip

MCQ

Identify the correct statement :

A
If system of $n$ simultaneous linear equations has $a$ unique solution, then coefficient matrix is singular
✓
If system of $n$ simultaneous linear equations has $a$ unique solution, then coefficient matrix is non singular
C
If $A^{-1}$ exists , $(adjA)^{-1}$ may or may not exist
D
$F(x) =$ $\left[ {\begin{array}{*{20}{c}}{\cos x}&{ - \sin x}&0\\{\sin x}&{\cos x}&0\\0&0&0\end{array}} \right]$, then $F(x) . F(y) = F(x - y)$

✓

Answer

Correct option: B.

If system of $n$ simultaneous linear equations has $a$ unique solution, then coefficient matrix is non singular

b
$(A)$ It should be non singular
$(B)$ since $A^{-1} =$ $\frac{{adj\,A}}{{|A|}}$ , hence adj $A$ must be a non singular matrix. Its inverse must exist.
$(D)$ It should be $F( x + y)$

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